Squarylium dye with two propyl and two hexyl groups forms a mono-molecular layer with domains of J-aggregates by spreading its chloroform solution at an air-water interface. Fluorescence microscopy and an absorbance evaluation which also considers the reflectance suggest that this Langmuir-film has a close packed two-dimensional structure with a complete Jaggregate formation of all dye molecules. Strong and ultrafast nonlinear optical responses, indicating delocalization of excitons over 30 molecules, have been observed at 5 °C from this ideal mono-molecular layer of J-aggregates.